XY-Chain

Expert

A chain of bivalue cells; the common candidate at both ends can be eliminated from cells seeing both ends.

How It Works

A chain formed by bivalue cells connected through shared candidates. The candidate common to both ends of the chain can be eliminated from any cell seeing both endpoints.

This is the generalization of XY-Wing: an XY-Wing is simply a 3-cell XY-Chain. Longer chains are more powerful but harder to find.

Example

34
34
9715628
1
25
25
689347
68
67
678
234159
26
26
1573894
358
35
358
496271
794128536
24
8
27
951
47
63
56
1
56
347982
9
347
37
862
47
15
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Hard25 givensStrict